In the prior art, there has been developed a machine for grinding concrete, stone and other like surfaces which generally consists of a motor mounted in a housing provided with a handle, a planetary disk mounted on an output shaft of such motor and a plurality of grinding head units mounted on the planetary disk and rotatable therewith. Typically, each of such head units is provided with a circular holder disk and a consumable, circular grinding disk detachably mountable on an underside of the holder disk. In such machines, the grinding disks may be replaced simply by manually detaching a worn disk and attaching a new disk. In doing so, it is advisable to mount the replacement disk concentrically on the holder disk. Otherwise, an eccentrically mounted replacement disk may adversely affect the operation of the machine, the attachment of the grinding disk to the holder disk, the effectiveness of the grinding disk and/or the condition of the surface being worked. In view of such possible misalignment of a consumable grinding disk during the replacement of a worn disk, it has been found to be desirable to provide for an improved arrangement for properly mounting replacement disks on the holder disks of such machines. Accordingly, it is the principal object of the present invention to provide for such an improved arrangement.